Vibrations of the Dissymmetry Planetary Gears

The position of the planets for the planetary gear systems are in two forms of equally and unequally spaced. This paper investigates free vibration of the planetary gear with unequally spaced planets. The planetary gear set of this study is modeled as set of lumped masses and springs. Each component such as sun gear, carrier, ring gear and planets possesses three degrees of freedom and considered as rigid bodies. Bearing and mesh stiffnesses are modeled in the form of linear springs. Generally, planet, rotational, translational, distinct and degenerate modes are five vibration modes of the planetary gear systems. The results show that the translational mode for the system with numbers of even equally and unequally spaced planets, is different and rotational and translational modes have the same characteristics for the both systems. For the system with numbers of even unequally spaced planets, the natural frequencies of the translational modes have multiplicity one. When the numbers of the planets of the system are odd and the position of them is unequally spaced, the rotational and planet modes are generating and the natural frequencies of the translational modes are not appears. For the distinct and degenerate modes of the system with unequally spaced planets, the planets only have the rotational motion.